Comment to the note "Counting of discrete Rossby/drift wave resonant triads", arXiv:1309.0405
A. Kartashov, E. Kartashova
TL;DR
This paper clarifies a misunderstanding in a previous note regarding the counting of resonant triads, emphasizing that wave amplitudes are complex, not real, as previously assumed.
Contribution
It corrects the misconception in arXiv:1309.0405 by highlighting the complex nature of wave amplitudes in resonant triads.
Findings
Resonant triads have complex wave amplitudes.
The previous note erroneously assumed real amplitudes.
Clarification impacts the counting of resonant triads.
Abstract
The main purpose of this note is clarify the following misunderstanding apparent in the note arXiv:1309.0405 by M. Bustamante, U. Hayat, P. Lynch, B. Quinn; [1]: the authors erroneously assume that in the manuscript arXiv:1307.8272 by A. Kartashov and E. Kartashova, [2], resonant triads with real amplitudes are counted whereas it can be seen explicitly from the form of dynamical system that wave amplitudes are complex.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Dynamics and Pattern Formation · Nonlinear Waves and Solitons